1. Field of the Invention
The present invention relates to channel estimation and equalization in a wireless communication system, and more specifically, to channel estimation using decision feedback.
2. Description of the Related Art
The modulation algorithm employed in both Global System for Mobile (GSM) and General Packet Radio System (GPRS) communication networks is Gaussian Minimum Shift Keying (GMSK), which induces inter-symbol interference (ISI) in the received signal sampled. ISI is the residual effect of other neighboring symbols when decoding a certain symbol, and this residual effect is due to the occurrence of pulses before and after the sampling instant. The unavoidable presence of ISI in the system, however, introduces errors in the decision device at the receiver output. Therefore, in the filter design of the GSM/GPRS receiver and transmitter, the objective is to diminish the effects of ISI and thereby deliver the digital data to the destination with the smallest error rate possible. An equalizer is a widely used approach for compensating or reducing the ISI effect.
An exemplary transmission model of a wireless communication system is shown in FIG. 1. A signal 21 from the transmitter 22 is first filtered by a Low Pass (LP) filter 221, converted to radio frequency (RF) by multiplying a carrier in a multiplier 222, and finally passed to a processing unit 223 before transmission to the channel 24. The processing unit 223 extracts the real part of the signal. The characteristic of the channel 24 is modeled by a channel response block 241 with channel noise 23. The channel noise 23 is generally assumed as Additive White Gaussian Noise (AWGN). The multiplier 261 in the receiver 26 converts back the frequency of the signal received by the receiver by multiplying the same frequency as the carrier frequency. The LP filter 262 receives the down converted signal, and outputs a received signal 25. The equalizer 263 compensates the ISI of the received signal 25, and outputs an estimated signal 27. The received signal r(t) 25 is expressed by Equation [1]. Channel response g(t), filter response ft(t) of the transmitter 22, and filter response fr(t) of the receiver 26 can be combined as a channel impulse response h(t) which models the response of the transmission channel including the transmitting and receiving ends. The channel impulse response h(t) is the convolution of ft(t), g(t), and fr(t).
                              r          ⁡                      (            t            )                          =                                            ∑              n                        ⁢                                          a                n                            ⁢                              h                ⁡                                  (                                      t                    -                                          n                      ⁢                                                                                          ⁢                      T                                                        )                                                              +                      n            ⁡                          (              t              )                                                          Equation        ⁢                                  [        1        ]            
The channel noise n(t) 23 herein is assumed to be stationary Gaussian noise with zero mean and variance No. Let {αn} (which is also the signal 21 in FIG. 1) be a hypothetical sequence of pulse amplitudes transmitted during a time period I. The equalizer 263 is assumed to be a Maximum Likelihood (ML) equalizer, which determines the best estimation of {αn} as the estimated sequence {ân} (signal 27 of FIG. 1). The estimated sequence {αn}={ân} is derived by maximizing the likelihood function as shown in Equation [2].p[r(t),tεI|{αn}]  Equation [2]
The probability of 0s and 1s in the transmitted sequences are assumed to be equal, therefore, Equation [2] can be rewritten as:
                              p          ⁡                      [                                          {                                  α                  n                                }                            |                              r                ⁡                                  (                  t                  )                                                      ]                          =                                            p              ⁡                              (                                                      r                    ⁡                                          (                      t                      )                                                        |                                      {                                          α                      n                                        }                                                  )                                      ⁢                          p              ⁡                              (                                  {                                      α                    n                                    }                                )                                                          p            ⁡                          (                              r                ⁡                                  (                  t                  )                                            )                                                          Equation        ⁢                                  [        3        ]            
p[{αn}|r(t)] is also called the posteriori probability. The probability of the estimated sequence p[{αn}] and the received signal r(t) are both assumed to be constant. Since the objective of the ML equalizer is to maximize the likelihood function shown in Equation [2], the posteriori probability must also be maximized. If the sequence {αn} was the actual sequence of the pulse amplitude transmitted during time period I, the power density function of the noise signal n(t) can be expressed as shown in Equation [4].
                                          n            ⁡                          (                              t                |                                  {                                      α                    n                                    }                                            )                                =                                    r              ⁡                              (                t                )                                      -                                          ∑                                  nT                  ∈                  I                                            ⁢                                                α                  n                                ⁢                                  h                  ⁡                                      (                                          t                      -                      nT                                        )                                                                                      ,                  t          ∈          I                                    Equation        ⁢                                  [        4        ]            
The ML function of Equation [2] thus becomes:
                              p          ⁡                      (                                          r                ⁡                                  (                  t                  )                                            |                              {                                  α                  n                                }                                      )                          =                              p            ⁡                          [                                                n                  ⁡                                      (                    t                    )                                                  |                                  {                                      α                    n                                    }                                            ]                                =                                                    (                                  1                                      2                    ⁢                    π                    ⁢                                                                                  ⁢                                          N                      o                                                                      )                            N                        ⁢                          exp              ⁡                              (                                                                            -                                              1                                                  2                          ⁢                                                      N                            o                                                                                                                ⁢                                                                  ∑                                                  k                          =                          1                                                                    N                                                        |                                                            r                      k                                        -                                                                  ∑                        n                                            ⁢                                                                        α                          n                                                ⁢                                                  h                          kn                                                                                                      ⁢                                      |                    2                                                  )                                                                        Equation        ⁢                                  [        5        ]            
The probability of the ML function p[r(t)|{αn}] is proportional to the logarithm of p[r(t)|{αn}]:
                              -                                    ∫                              -                ∞                            ∞                        ⁢                                                                                                                        r                      ⁡                                              (                        t                        )                                                              -                                                                  ∑                        n                                            ⁢                                                                        α                          n                                                ⁢                                                  h                          ⁡                                                      (                                                          t                              -                              nT                                                        )                                                                                                                                                                2                            ⁢                                                          ⁢                              ⅆ                t                                                    =                              -                                          ∫                                  -                  ∞                                ∞                            ⁢                                                                                                              r                      ⁡                                              (                        t                        )                                                                                                  2                                ⁢                                  ⅆ                  t                                                              +                      2            ⁢            Re            ⁢                                          ∑                n                            ⁢                              [                                                      α                    n                    *                                    ⁢                                                            ∫                                              -                        ∞                                            ∞                                        ⁢                                                                  r                        ⁡                                                  (                          t                          )                                                                    ⁢                                                                        h                          *                                                ⁡                                                  (                                                      t                            -                            nT                                                    )                                                                    ⁢                                              ⅆ                        t                                                                                            ]                                              -                                    ∑              n                        ⁢                                          ∑                m                            ⁢                                                α                  n                  *                                ⁢                                  α                  m                                ⁢                                                      ∫                                          -                      ∞                                        ∞                                    ⁢                                                                                    h                        *                                            ⁡                                              (                                                  t                          -                          nT                                                )                                                              ⁢                                          h                      ⁡                                              (                                                  t                          -                          mT                                                )                                                              ⁢                                          ⅆ                      t                                                                                                                              Equation        ⁢                                  [        6        ]            
The first term of Equation [6] is a constant, thus it can be discarded when calculating the metric. A correlation metrics (MC) can be derived from the previous steps as shown in Equation [7].
                                          CM            ⁡                          (                              {                                  α                  1                                }                            )                                =                                    2              ⁢                                                          ⁢              Re              ⁢                                                ∑                                      nT                    ∈                    I                                                  ⁢                                  (                                                            α                      n                      *                                        ⁢                                          Z                      n                                                        )                                                      -                                          ∑                                  iT                  ∈                  I                                            ⁢                                                ∑                                      kT                    ∈                    I                                                  ⁢                                                      α                    n                    *                                    ⁢                                      α                    k                                    ⁢                                      s                                          i                      -                      k                                                                                                          ⁢                                  ⁢                  where          ⁢                                          ⁢                                                                                          z                    n                                    =                                                                                                                                          g                            MF                                                    ⁡                                                      (                            t                            )                                                                          *                                                  r                          ⁡                                                      (                            t                            )                                                                                              ⁢                                              |                                                  t                          =                          nT                                                                                      =                                                                                            ∑                          l                                                ⁢                                                                              a                                                          n                              -                              1                                                                                ⁢                                                      s                            l                                                                                              +                                              w                        n                                                                                                                                                                                      s                    l                                    =                                                                                                                                          g                            MF                                                    ⁡                                                      (                            t                            )                                                                          *                                                  h                          ⁡                                                      (                            t                            )                                                                                              ⁢                                              |                                                  t                          =                          lT                                                                                      =                                                                  s                                                  -                          l                                                *                                            ⁢                                                                                          ⁢                      and                                                                                                                                                                                      g                      MF                                        ⁡                                          (                      t                      )                                                        =                                                            h                      *                                        ⁡                                          (                                              -                        t                                            )                                                                                                                              Equation        ⁢                                  [        7        ]            
s1 herein is the channel response autocorrelation.
Maximum Likelihood Sequence Estimation (MLSE) determines the most likely sequence originally transmitted by the sequence {αn} by maximizing the likelihood function shown in Equation [5], or equivalently, maximizing the metric shown in Equation [8].
                                          J            n                    ⁡                      (                          {                              α                I                            }                        )                          =                              2            ⁢                                                  ⁢            Re            ⁢                                          ∑                                  nT                  ∈                  I                                            ⁢                              (                                                      α                    n                    *                                    ⁢                                      Z                    n                                                  )                                              -                                    ∑                              iT                ∈                I                                      ⁢                                          ∑                                  kT                  ∈                  I                                            ⁢                                                α                  i                  *                                ⁢                                  s                                      i                    -                    k                                                  ⁢                                  α                  k                                                                                        Equation        ⁢                                  [        8        ]            
The MLSE algorithm obtained represents a modified version of the well-known Viterbi algorithm. The Viterbi algorithm is obtained by computing the recursive relation iteratively.
                                          J            n                    (                                          ⁢                      …            ⁢                                                  ,                          α                              n                =                1                                      ,                          α              n                                )                =                                            J                              n                -                1                                      (                                                  ⁢                          …              ⁢                                                          ,                              α                                  n                  -                  1                                                      )                    +                      Re            ⁡                          [                                                α                  n                  *                                ⁡                                  (                                                            2                      ⁢                                              Z                        n                                                              -                                                                  s                        0                                            ⁢                                              α                        n                                                              -                                          2                      ⁢                                                                        ∑                                                      k                            ≤                                                          n                              -                              1                                                                                                      ⁢                                                                              s                                                          n                              -                              k                                                                                ⁢                                                      α                            k                                                                                                                                )                                            ]                                                          Equation        ⁢                                  [        9        ]            
FIG. 2 shows the architecture of the Viterbi Equalizer, wherein the received signal r(t) is estimated according to Equation [1].
FIG. 3 is a block diagram showing iterative channel estimation and equalization. The channel impulse response estimated by the channel estimator 34 must be updated frequently to maintain the accuracy of the estimation. There are several well known techniques such as Least Square (LS) and Minimum Mean Square Estimation (MMSE) using decision feedback circuit to achieve better estimation of channel impulse response. As shown in FIG. 3, the initial channel estimation is obtained by passing a training sequence to the channel estimator 34. After a block of data is equalized in the equalizer 32, the output is fed back to the adaptive channel estimator 34 to generate a better estimation for the equalizer 32. Such channel estimation and equalization procedures are performed iteratively to adapt variable transmission channel conditions. The equalizer 32 outputs either hard value decisions according to Hard Output Viterbi Algorithm (HOVA) or soft value decisions according to Soft Output Viterbi Algorithm (SOVA) to the channel estimator 34 and decoder 36.
It is assumed that the number of channel taps is L and the received signal r consists of N samples. The received signal can be expressed as:r=Bh+n   Equation [10]
where B is the matrix with the transmitted bits, h is the channel, and n is the channel noise. The matrix product Bh corresponds to the convolution between bk and hk. From the LS algorithm, the channel can be estimated as:ĥLS=(BHB)−1BHr   Equation [11]
where OH denotes Hermitian transpose.
For HOVA, the channel is estimated as:
                                                        h              ^                        m            HO_LS                    =                                                    (                                                      B                    H                                    ⁢                  B                                )                                            -                1                                      ⁢                                                            ∑                                      k                    =                                          L                      -                      1                                                                                        N                  -                  1                                            ⁢                                                r                  k                                ⁢                                  b                                      k                    -                    m                                                                                      ,                              b            k                    =                      ±            1                                              Equation        ⁢                                  [        12        ]            
For SOVA, the channel is estimated as:
                                                        h              ^                        m            SO_LS                    =                                                    (                                                      B                    H                                    ⁢                  B                                )                                            -                1                                      ⁢                                                            ∑                                      k                    =                                          L                      -                      1                                                                                        N                  -                  1                                            ⁢                                                r                  k                                ⁢                                  b                                      k                    -                    m                                                                                      ⁢                                  ⁢                                  ⁢        where        ⁢                                  ⁢                                  ⁢                              b            k                    =                                    E              ⁢                              {                                                      b                    k                                    |                  r                                }                                      =                                                            2                  ⁢                  P                  ⁢                                      {                                                                  b                        k                                            =                                                                        +                          1                                                |                        r                                                              }                                                  -                1                            =                              tanh                ⁡                                  (                                                            L                      (                                                                        b                          k                                                |                        r                                                              2                                    )                                                                    ⁢                                  ⁢                              L            ⁡                          (                                                b                  k                                |                r                            )                                =                      log            ⁢                                          Pr                ⁡                                  (                                                            b                      k                                        =                                                                  +                        1                                            |                      r                                                        )                                                            Pr                ⁡                                  (                                                            b                      k                                        =                                                                  -                        1                                            |                      r                                                        )                                                                    ⁢                                  ⁢                              Pr            ⁡                          (                                                b                  k                                =                                                      +                    1                                    |                  r                                            )                                =                                    ⅇ                              L                ⁡                                  (                                                            b                      k                                        |                    r                                    )                                                                    1              +                              ⅇ                                  L                  ⁡                                      (                                                                  b                        k                                            |                      r                                        )                                                                                                          Equation        ⁢                                  [        13        ]            
Various techniques in the art focus on the method of achieving better channel impulse estimation using decision feedback. The Least Square (LS) technique is used here as an example to illustrate the channel estimation operation, while other techniques omitted herein as the method provided in the present invention does not teach a way of estimating channel impulse response. The present invention focuses on determining whether decision feedback is required for the channel estimator to achieve a better channel estimation for the equalizer.